Part I Dynamics of Particles 1 1 Introduction to Dynamics 3 1/1 History and Modern Applications 3 1/2 Basic Concepts 4 1/3 Newton’s Laws 5 1/4 Units 6 1/5 Gravitation 7 1/6 Dimensions 10 1/7 Solving Problems in Dynamics 11 1/8 Chapter Review 13 2 Kinematics of Particles 16 2/1 Introduction 16 2/2 Rectilinear Motion 17 2/3 Plane Curvilinear Motion 25 2/4 Rectangular Coordinates (x-y) 27 2/5 Normal and Tangential Coordinates (n-t) 32 2/6 Polar Coordinates (r-𝜽) 37 2/7 Space Curvilinear Motion 42 2/8 Relative Motion (Translating Axes) 47 2/9 Constrained Motion of Connected Particles 51 2/10 Chapter Review 54 3 Kinetics of Particles 56 3/1 Introduction 56 Section A Force, Mass, and Acceleration 57 3/2 Newton’s Second Law 57 3/3 Equation of Motion and Solution of Problems 60 3/4 Rectilinear Motion 62 3/5 Curvilinear Motion 67 Section B Work and Energy 71 3/6 Work and Kinetic Energy 71 3/7 Potential Energy 81 Section C Impulse and Momentum 87 3/8 Introduction 87 3/9 Linear Impulse and Linear Momentum 87 3/10 Angular Impulse and Angular Momentum 93 Section D Special Applications 99 3/11 Introduction 99 3/12 Impact 99 3/13 Central-Force Motion 105 3/14 Relative Motion 112 3/15 Chapter Review 118 4 Kinetics of Systems of Particles 119 4/1 Introduction 119 4/2 Generalized Newton’s Second Law 120 4/3 Work-Energy 121 4/4 Impulse-Momentum 122 4/5 Conservation of Energy and Momentum 126 4/6 Steady Mass Flow 132 4/7 Variable Mass 138 4/8 Chapter Review 144 Part II Dynamics of Rigid Bodies 145 5 Plane Kinematics of Rigid Bodies 147 5/1 Introduction 147 5/2 Rotation 149 5/3 Absolute Motion 154 5/4 Relative Velocity 158 5/5 Instantaneous Center of Zero Velocity 165 5/6 Relative Acceleration 168 5/7 Motion Relative to Rotating Axes 173 5/8 Chapter Review 183 6 Plane Kinetics of Rigid Bodies 184 6/1 Introduction 184 Section A Force, Mass, and Acceleration 186 6/2 General Equations of Motion 186 6/3 Translation 192 6/4 Fixed-Axis Rotation 196 6/5 General Plane Motion 199 Section B Work and Energy 205 6/6 Work-Energy Relations 205 6/7 Acceleration from Work-Energy; Virtual Work 213 Section C Impulse and Momentum 217 6/8 Impulse-Momentum Equations 217 6/9 Chapter Review 225 7 Introduction to Three-Dimensional Dynamics of Rigid Bodies 226 7/1 Introduction 226 Section A Kinematics 227 7/2 Translation 227 7/3 Fixed-Axis Rotation 227 7/4 Parallel-Plane Motion 228 7/5 Rotation about a Fixed Point 228 7/6 General Motion 234 Section B Kinetics 240 7/7 Angular Momentum 240 7/8 Kinetic Energy 243 7/9 Momentum and Energy Equations of Motion 246 7/10 Parallel-Plane Motion 248 7/11 Gyroscopic Motion: Steady Precession 250 7/12 Chapter Review 259 8 Vibration and Time Response 260 8/1 Introduction 260 8/2 Free Vibration of Particles 261 8/3 Forced Vibration of Particles 270 8/4 Vibration of Rigid Bodies 278 8/5 Energy Methods 282 8/6 Chapter Review 286 Appendix A Area Moments of Inertia 287 Appendix B Mass Moments of Inertia 288 B/1 Mass Moments of Inertia about an Axis 288 B/2 Products of Inertia 296 Appendix C Selected Topics of Mathematics 302 C/1 Introduction 302 C/2 Plane Geometry 302 C/3 Solid Geometry 303 C/4 Algebra 303 C/5 Analytic Geometry 304 C/6 Trigonometry 304 C/7 Vector Operations 305 C/8 Series 308 C/9 Derivatives 308 C/10 Integrals 309 C/11 Newton’s Method for Solving Intractable Equations 312 C/12 Selected Techniques for Numerical Integration 314 Appendix D Useful Tables 317 Table D/1 Physical Properties 317 Table D/2 Solar System Constants 318 Table D/3 Properties of Plane Figures 319 Table D/4 Properties of Homogeneous Solids 321 Table D/5 Conversion Factors; SI Units 325 Problems P-1 Index I-1 Problem Answers PA-1